With the development of radio and space technologies, several satellites based navigation systems have already been built and more will be in use in the near future. One example of such satellites based navigation systems is Global Positioning System (GPS), which is built and operated by the United States Department of Defense. The system uses twenty-four or more satellites orbiting the earth at an altitude of about 11,000 miles with a period of about twelve hours. These satellites are placed in six different orbits such that at any time a minimum of six satellites are visible at any location on the surface of the earth except in the polar region. Each satellite transmits a time and position signal referenced to an atomic clock. A typical GPS receiver locks onto this signal and extracts the data contained in it. Using signals from a sufficient number of satellites, a GPS receiver can calculate its position, velocity, altitude, and time.
A GPS receiver has to acquire and lock onto at least four satellite signals in order to derive the position and time. Usually, a GPS receiver has many parallel channels with each channel receiving signals from one visible GPS satellite. The acquisition of the satellite signals involves a two-dimensional search of carrier frequency and the pseudo-random number (PRN) code phase. Each satellite transmits signals using a unique 1023-chip long PRN code, which repeats every millisecond. The receiver locally generates a replica carrier to wipe off residue carrier frequency and a replica PRN code sequence to correlate with the digitized received satellite signal sequence. During the acquisition stage, the code phase search step is a half-chip for most navigational satellite signal receivers. Thus the full search range of code phase includes 2046 candidate code phases spaced by a half-chip interval. The carrier frequency search range depends upon the Doppler frequency due to relative motion between the satellite and the receiver. Additional frequency variation may result from local oscillator instability.
Coherent integration and noncoherent integration are two commonly used integration methods to acquire GPS signals. Coherent integration provides better signal gain at the cost of larger computational load, for equal integration times.
The power associated with noncoherent integration with one millisecond correlation is
  Power  =            ∑              n        =        0                    N        -        1              ⁢          (                                    I            ⁡                          (              n              )                                2                +                              Q            ⁡                          (              n              )                                2                    )      and the power associated with coherent integration is
  Power  =                    (                              ∑                          n              =              0                                      N              -              1                                ⁢                      I            ⁡                          (              n              )                                      )            2        +                  (                              ∑                          n              =              0                                      N              -              1                                ⁢                      Q            ⁡                          (              n              )                                      )            2      where I(n) and Q(n) denote the in-phase and quadra-phase parts of one-millisecond correlation values from the baseband section at interval n, and N denotes the desired number of one-millisecond integration intervals.
The signals from the navigational satellites are modulated with navigational data at 50 bits/second. This data consists of ephemeris, almanac, time information, clock and other correction coefficients. This data stream is formatted as sub-frames, frames and super-frames. A sub-frame consists of 300 bits of data and is transmitted for 6 seconds. In this sub-frame a group of 30 bits forms a word with the last six bits being the parity check bits. As a result, a sub-frame consists of 10 words. A frame of data consists of five sub-frames transmitted over 30 seconds. A super-frame consists of 25 frames sequentially transmitted over 12.5 minutes.
The first word of a sub-frame is always the same and is known as TLM word and first eight bits of this TLM word are preamble bits used for frame synchronization. A Barker sequence is used as the preamble because of its excellent correlation properties. The other bits of this first word contains telemetry bits and is not used in the position computation. The second word of any frame is the HOW (Hand Over Word) word and consists of TOW (Time Of Week), sub-frame ID, synchronization flag and parity with the last two bits of parity always being ‘0’s. These two ‘0’s help in identifying the correct polarity of the navigation data bits. The words 3 to 10 of the first sub-frame contains clock correction coefficients and satellite quality indicators. The 3 to 10 words of the sub-frames 2 and 3 contain ephemeris. These ephemeris are used to precisely determine the position of the GPS satellites. These ephemeris are uploaded every two hours and are valid for four hours to six hours. The 3 to 10 words of the sub-frame 4 contain ionosphere and UTC time corrections and almanac of satellites 25 to 32. These almanacs are similar to the ephemeris but give a less accurate position of the satellites and are valid for six days. The 3 to 10 words of the sub-frame 5 contain only the almanacs of different satellites in different frames.
The ephemeris are used in the computation of the position of the satellites at a given time. The accuracy of the computed receiver position depends upon the accuracy of the satellite positions which in-turn depends upon the age of the ephemeris. The use of current ephemeris results in better position estimation than one based on non-current or obsolete ephemeris. Therefore it is necessary to use current ephemeris to get a precise receiver position.
A GPS receiver may acquire the signals and estimate the position depending upon the already available information. In the ‘hot start’ mode the receiver has current ephemeris and the position and time are known. In another mode known as ‘warm start’ the receiver has non-current ephemeris but the initial position and time are known as accurately as the in the case of previous ‘hot start’. In the third mode, known as ‘cold start’, the receiver has no knowledge of position, time or ephemeris. As expected the ‘hot start’ mode results in low Time-To-First-Fix (TTFF) while in the ‘warm start’ mode the receiver may wait to download new ephemeris which may take more than eighteen seconds. The ‘cold start’ takes still more time for the first position fix as there is no data available to aid signal acquisition and position fix.
It is not always possible to maintain a copy of current ephemeris in the receiver. The reason may be that the receiver had no opportunity to download the ephemeris as it might have been in a powered off state for longer than four hours or because the received signal is very weak. Under these cases it is desirable to develop techniques to obtain better positioning accuracy with non-current ephemeris to reduce the warm start time. There are U.S. patents that disclose methods of fast signal acquisition in the presence of non-current ephemeris. U.S. Pat. No. 6,429,809, 6,707,420, 6,930,635, and published U.S. patent applications 2002/0154056, 2002/0149516, 2002/0130812, and 2003/0112176 by Qualcomm disclose methods for sending additional aiding information to receivers to provide correction due to the use of old ephemeris. U.S. Pat. No. 6,727,848 and U.S. patent application 2002/0186165 disclose aiding by a reference receiver or through DGPS. When aided by the reference receiver, the required correction is generated at the remote reference receiver. U.S. Pat. No. 6,225,945 assigned to Trimble Corp. obtains the position correction by integrating the velocity. While this method does not require current ephemeris for the computation of correction, it is less accurate. Thus, these methods require additional aiding stations or involve computation and may be less accurate.
Therefore, there is a need for methods and systems that enable a mobile navigation receiver to accurately determine its trajectory with non-current ephemeris in stand-alone mode and does not require a large computation load.